| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB282000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析学Ｂ |
Subject Name
（Katakana） |
スウリカイセキガクB |
Subject Name in
English |
Mathematical Analysis B |
| Instructor |
KAMIMOTO SHINGO |
Instructor
(Katakana) |
カミモト シンゴ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Mon7-8,Weds3-4：SCI E210 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Lectures are given face-to-face or online depending on the situation. |
| Credits |
2.0 |
Class Hours/Week |
|
Language of Instruction |
B
:
Japanese／English |
| Course Level |
4
:
Undergraduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Holomorphic functions of several variables, Analytic differential equation, Regular singular point, The Cauchy-Kowalewski theorem, Zerner's theorem. |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | Mathematics
（Knowledge and Understanding）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. |
|---|
Class Objectives
/Class Outline |
We learn the basics of the theory of analytic differential equations. |
| Class Schedule |
lesson1 Power series and the domain of convergence
lesson2 Radius of convergence
lesson3 Holomorphic functions of several variables
lesson4 Cauchy's integral representation
lesson5 Existence and uniqueness of solutions of analytic ordinary differential equations
lesson6 Analytic continuation of solutions of ordinary differential equations
lesson7 Analytic solutions of linear ordinary differential equations
lesson8 Monodromy representations
lesson9 Regular singular points
lesson10 The Frobenius method
lesson11 Initial value problem for partial differential equations
lesson12 The Cauchy-Kowalewski theorem
lesson13 Zerner's theorem
lesson14 Bicharacteristic strip
lesson15 Propagation of singularity |
Text/Reference
Books,etc. |
If you can read Japanese books, please check the syllabus of this course written in Japanese. Otherwise, please consult at the classroom. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Black board |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Lesson1 - Lesson4 Understand fundamental properties of holomorphic functions of several variables.
Lesson5 - Lesson8 Study properties of analytic solutions of analytic ordinary differential equations.
Lesson9 - Lesson10 Study behaviors of solutions at singular points.
Lesson11 - Lesson15 Study analyticity of solutions of analytic partial differential equations. |
| Requirements |
|
| Grading Method |
Reports (90%), Class participation (10%). |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |